On my 2000, 2500 Cummins all original:

First, my right turn signal gives me a very fast blink and the right rear turn lamp doesn't come on. Is that just a burned out bulb? How do you get to it to change it?

The truck has 150,000 on it. Always serviced on the ranch and regularly. Nothing ever done to it but U joints and tires. It runs and looks good. Is there anything that should be done to the engine with that number of miles on it? What about the turbo? Does it need looked at?

 

all you need to do is replace the bulb (if it is indeed burned out) Drop the tail gate and you should see a coupla screws on the side of the tail light. pull them out and your tail light will come out. Then twist the plug and pull, this will release it from the housing.

as long as its been reguarly maintaned, then no, its just fine. make sure its all greased and good to go

 

At 150k a valve adjustment would be a good idea.

 

Agreed, it's overdue for valve adj.
Also fuel pressure check, very important on the 24 valve, you really should have a gauge.
Change out all the fluids, trans and diffs included, and fan belt.
Enjoy another couple hundred thousand miles.

 

the fast blink is due to the decreased power drawn from the circuit because of the rear bulb not lighting. Change the bulb out and you should be good to go. Check for voltage at the bulb socket just to make sure a wire didnt break or come loose, but my moneys on it just being a simple bulb. Slap a new bulb in and run her for another 150k miles! Fuel gauges are worth their weight in gold, and relatively inexpensive (price out a new vp44 for comparison). Definitely worth it in my opinion to avoid high cost repairs, especially if the truck "has to work."

 

ZD, if your truck is the same as my 2002, the tail light has two torqux screws, and the pulls streight out to the rear. The tail/stop are 3157 bulbs, same as the bulb for the backup light. So I have swapped BU bulb with tail/stop untill I got a new bulb, A 2 minuite quck fix, even for me.
Happy nNew Year and welcome to the site.